SU1297009A1 - Adaptive control system for objects with delaying - Google Patents

Abstract

The invention relates to systems of automatic control of objects with non-stationary dynamic characteristics, including latency, and can be used in industry and in the study of the characteristics of objects with unknown parameters. The purpose of the invention is to improve the quality of control and expansion of functionality. Adaptive control system with a delay contains a setpoint 1, a comparison element 2, a control top 3, a control object 4, a block 5 of analog-digital converters, a block 6 of identifying parameters of a mathematical model of a control object, a block 7 calculating weight functions based on a high-pore model yes, block 8 for calculating weight functions from a low-order model, block 9 for finding the error function, block 10 for estimating the real object lag time, block 11 for estimating parameters of a low-order model, block 12 for adjusting the coefficients of registers street torah. The purpose of the invention is achieved by the introduction of blocks 5-12. 1 il. from 9 to to about about with

Description

The invention relates to systems for the automatic control of objects with non-stationary dynamic characteristics, including latency, and can be used for adaptive control in various industries and in the study of the characteristics of objects with unknown parameters.

The aim of the invention is to improve the quality of control and expansion of functionality.

The drawing shows a functional diagram of the system of adaptive control of objects with variable behind the lag.

The system contains a setting device 1, a comparison element 2, a controller 3, a control object 4, an analog-to-digital converter unit 5, a parameter .6 parameter identification block for a mathematical model of the control object, a block 7 for calculating object weight functions from a high-order model, a block 8 for calculating weight object functions by the low-order model, unit 9 for finding the error function, unit 10 for estimating the true object lag time, unit 11 for estimating the parameters for the Low-order Model, unit 12 for adjusting the controller coefficients.

The adaptive control system consists of two circuits and operates in the following manner.

The first circuit contains the setting device 1, the reference element 2, the controller 3 and the control object 4. The first input of the regulator 3 receives an error Regulatory circuit is designed to adjust the coefficients of the regulator in accordance with the change of the dynamic characteristics of the object and contains blocks 5-12. The inputs of block 5 receive analog signals from the input and output of the object, as well as the measured disturbance, which are converted into digital form and fed to the input of the block 6 for identifying the parameters of the object model in the form

h

Do ya y +111. + ZIIc.V

 7ГГ - trr tr 7

thirty

(3)

35

according to law

where V is the measured perturbation on

the entrance of the object; but,

with. - coefficients of polynomials of the autoregressive moving average model.

The order of the polynomials A, C is m 2.3; the order of the polynomial B is equal to m + d, where c1 is the maximum possible time lag of the object, from the output of element 2 versus Q, it implements the estimation procedure that is used to express the coefficients a-., b V, c. on each control action in the co-sampling period according to

with new measurements of input, output

.. / f perturbing an object using racy LR (Y,) - F (k + d, k} J / Q, (1) j of the conventional recurrent method for measuring input and output 1, least squares. The model (3) takes into account all possible values of the delay time EI of the experimentally determined range of values of d from 50 to zero d, but it is not suitable for calculating the controller coefficients due to the high order. The computational procedure becomes too complicated. Therefore, a low order of exit of the object, op-, "" "about

where and

Y -

SK d

object at time k; the regulation error i is the discrete time delay of the object, equal to an integer number of measurement sampling periods, Ф (k + d ,, k) is the minimum squared optimal equation in the sense of minimum

mm + c /

oA (k + d, k) -E: f, Y., + 11: g.u.,. +

 “- & - b -.

i; 0

i 0

(four)

+) F / (k + d-i, k-i),

(2)

where f., g.

с - regulating factors adjusted according to the change of the dynamic characteristics of the object;

m is the order of the object model;

R, Q are the adjustment factors of the controller for the required accuracy and speed of tracking the task.

The second circuit is designed to adjust the coefficients of the controller in accordance with the change of the dynamic characteristics of the object and contains blocks 5-12. The inputs of block 5 receive analog signals from the input and output of the object, as well as the measured disturbance, which are converted into digital form and fed to the input of the block 6 for identifying the parameters of the object model in the form

h

Do ya y +111. + ZIIc.V

 7ГГ - trr tr 7

(3)

where V is the measured perturbation on

 “- & - b -.

(four)

where d is the estimate of the true object lag time. To estimate d, the method of calculating and comparing the weight functions of an object is used according to model (3) and model (4), and impulse characteristics are calculated for model d (4). ; in the range O, ..., the outputs of block 6 of the identification of the parameters of the object under assessment a., b, c. the coefficients of model (3) are fed to the inputs of blocks 7, 8, 11, and 12; In block 7, the weight function H (Z) (2) of the object is calculated as the inverse Z-transform of model (3), i.e.

h

LL - a b.

1 2 1

From the output of block 7, the samples of the weight function (5) are fed to the second inputs of the block 8 for calculating the weight function using a low-order model, the first 25 inputs of which are used to estimate the coefficients h

of individuals a, b. from block 6 identification. In block 8, an inverse Z transform procedure is implemented for the model (4), as a result of which the counts of the weight function for the low-order model (4) are determined

h, h ... h 0;

l

h

d + 1

... h.

 h

 h, - b.

hT + cr + i m + d + i

Weight functions (6) are calculated for the entire range of time values.

-L

delays O, ..., d - 1.

The samples of the weight functions calculated in blocks 7 and 8 are served in block 9 to: go to the error function S (d ;-), defined by the ratio .i l

Ps);

S (di)

Oh, k d; +1, ... d. + m; (7)

- one,

Ps -iv) s

 .one

L Vd, 0, ... d, de N T / T,;

T

uh

characteristic 95% of the steady state value i Tj is the sampling period.

95 -S. 55

- time to reach the transition

The values of the error function S (d p are received in block 10, where the minimum value is determined

S

. (d;) min {s (d.) 1, V – d.,. . .d, - 1.

The value d; at which S (dj) takes a min1 ".1value, is the desired estimate of the object's lag time. It is transmitted to the third input of block 11, to the second input of which podshots samples of the weight function H (Z) from block 7, and to the third - the coefficients a; from block 6. In block 11, estimates of the coefficients bj of model (4) are calculated in accordance with equations

35

40

45

50

55

20

25 30

b h; 1 1 d

b, t,,

(eight)

which, together with the estimate d of the delay time, are fed to the second inputs of the block 12 for adjusting the controller coefficients, the first inputs of which are the values of the coefficients 3; , c, from the identification block 6. In block 12, the coefficients f, g., C-o of the controller (2) are updated in accordance with the new coefficients i and model a. , 6, с-, which characterize the dynamics of an object at a given time. The coefficients of the controller fj, g, c and the estimate d of the delay time are fed to the second input of the controller 3, which implements the control law (1).

Thus, the closed loop control is adaptive with respect to the variable dynamic characteristics of the object, including the lag time, which contributes to a significant increase in the dynamic accuracy of the stabilization of the object's output at a given level.

The use of the invention allows to increase the dynamic accuracy of the adjustment of the output variable under the conditions of non-stationarity of the dynamic characteristics of the object and the influence of the measured input disturbances. The accuracy of controlling the output variable of an object under the conditions of a slow change in its dynamic characteristics is higher than the classical algorithm of the NCU by 20–40%.

formula

and

5 3 o

12

bratis

An adaptive object management system with a lag, containing a serially connected master, a reference element, a controller, a control object, the output of which is connected to the subtractive input of the comparison element, which in order to improve the quality of control and expand functionality An analog-to-digital converter unit was introduced, the first and second inputs of which are connected respectively to the input and output of the object, the third input to the disturbing input, and the outputs to the inputs of the unit identifying a mathematical model of control object parameters, whose outputs are connected to inputs of the block for calculating the weight functions of the object of high-order model calculating unit

Editor I.Rybchenko Order 779/50

Compiled by V. Bashkirov

Tehred A. Kravchuk Proofreader N. Korol

Circulation 864 Subscription VNIIPI USSR State Committee

for inventions and discoveries 113035, Moscow, Zh-35, Raushsk nab., 4/5

Production and printing company, Uzhgorod, st. Project, 4

1297009

the weight functions of the object according to the low-order model, the low-order model parameter evaluation unit, and the coefficient of adjustment of the controller coefficients,

the second inputs of which are connected to the outputs of the low-order model parameter evaluation unit, and the outputs are connected to the controller inputs, the outputs of the object weight function calculation block are

the low-order models are connected to the inputs of the error function nazkdeni unit, the second inputs of which are connected to the outputs of the unit for calculating the weight functions of the object according to the high model

the order and with the second inputs of the unit for calculating the weight functions of the object according to the low order model and the parameter estimation unit of the low order model, and the outputs with the inputs of the unit

estimates of the true object lag time, the outputs of which are connected to the third inputs of the Low Order Model Parameter Estimation Unit.

Claims (1)

Claim An adaptive control system for objects with a delay, containing a serially connected master, a comparison element, a regulator, a control object, the output of which is connected to the subtracting input of the comparison element, characterized in that, in order to improve the quality of control and expand the functionality, an analog- digital converters, the first and second inputs of which are connected respectively with the input and output of the object, the third input is with the input of the disturbing effect, and the outputs are with the inputs of the ID block parameter identification of the mathematical model of the control object, the outputs of which are connected to the inputs of the unit for calculating the weight functions of the object according to the high order model, the unit for calculating the weight functions of the object according to the low order model, the unit for evaluating the parameters of the low order model and the unit for adjusting the controller coefficients, 5 second inputs of which are connected to the outputs of the unit for evaluating the parameters of the low-order model, and the outputs with the inputs of the controller, the outputs of the unit for calculating the weight functions of the object according to 10 low-order models are connected to the inputs of the unit for finding the error function, the second inputs of which are connected to the outputs of the unit for calculating the weight functions of the object according to the high order 15 model and to the second inputs of the unit for calculating the weight functions of the object according to the low order model and the unit for evaluating the parameters of the low order model, and the outputs to the inputs of the unit 20 estimating the true delay time of an object whose outputs are connected to the third inputs of the unit for estimating the parameters of the Low Order model.